The present invention relates to a method for calibrating a measuring system based on at least one camera, for determining the position of an object in a reference three-dimensional coordinate system, with which the external and internal camera parameters are calibrated in various steps, and the position of the camera is determined using external measuring means.
Within the framework of the ever-increasing automation of method and production processes using manipulators, e.g., robots, it is necessary to determine the position of objects to be processed in three dimensions, exactly, and in an automated manner, so that the manipulators may grip the objects in a defined manner.
To this end, optical measuring systems are often used that record images of the objects in the working space of the manipulators and evaluate them using image processing, in order to ascertain the orientation of features of the recorded object. Before optical measuring systems of this type may operate, the optical recording systems and/or cameras must be calibrated in a geometric camera model, which is used as the basis for evaluating the images. For the calibration, “internal” camera parameters that relate to the lens properties of the camera and the relative orientation of the lens and the image sensor, e.g., CCD or CMOS sensor, and “external” camera parameters must be determined, which relate to the geometric position, and the position and orientation of the camera in three dimensions.
A large number of various calibration methods for calibrating the camera has been described. An overview of them is provided in the paper by R, Gerdes et. al., “Kalibrierung eines digitalen Bildverarbeitungssystems mit CCD-Kamera” [Calibrating a digital image processing system with a CCD camera], tm—Technisches Messen 60 (1993) 6 and 60 (1993) 7/8, R. Oldenbourg Verlag [publisher], in which classical approaches for calibration methods are described. Using an approach derived from photogrammetry, a complete model of the camera is created, and the model parameters are ascertained by evaluating point correspondences. The point coordinates are obtained by recording known two- or three-dimensional point configurations of a calibration body and assigning the image points to the corresponding scene points. The non-linear systems of equations that generally result are solved numerically using iterative searching methods. Calibration methods based on this approach typically require a great deal of computing power, but they also satisfy the highest requirements on accuracy. Furthermore, linear models are known, with which the computing-effort is reduced, but so is the level of accuracy that may be attained. Calibration methods of this type are usually too expensive for an industrial production line, however, and they may not be used in a time-saving and money-saving manner, due, in particular, to post-calibrations that often must be carried out during production. In addition, reasonable starting values for the iteration usually must be specified. This makes it difficult to carry out a fully-automated calibration during the on-going process.
A second group of calibration methods attempts to utilize basic physical and geometric conditions to subdivide the parameters of the camera model into individual groups and to ascertain them in separate, consecutive steps. Via this reduction of the parameters to be determined in one step, the computing effort is reduced considerably compared to an iterative search within the entire parameter space, while also ensuring that the same high level of accuracy may be attained. A method of this type is described, e.g., in the paper by Roger Y. Tsai, “A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses”, IEEE Journal of Robotics and Automation”, Vol. RA-3, No. 4, August 1987, according to which geometric conditions are used as the basis for moving the camera, so that camera parameters may be determined separately using simpler systems of equations. This means of attaining the object is not universally usable, however, due to the geometric limitation. It is also disadvantageous that a separate calibration body with certain geometric properties should be used to calibrate the camera. A calibration body of this type must be moved into the field of view of the camera outside of the normal working process. This represents a considerable intervention in the production process. To determine the external camera parameters, it is also necessary to know the position (position and orientation) of the calibration body in the measuring system. This requires a corresponding amount of effort for carrying out the measurement, e.g., using external measuring devices, and it requires that the calibration body be moved into place for the post-calibration in a manner that is reproducible with great accuracy.
Publication EP 1 143 221 A2 describes a similar method for determining the position of a coordinate system of a work piece in three-dimensional space, with which the work piece is recorded using at least two cameras calibrated in three dimensions in order to determine the spacial position of the work piece. The cameras are calibrated in a pin-hole camera model, and the method is intended to be carried out without the use of calibration tables. To this end, when the camera is calibrated, the position and orientation of the radiation entrance window of each camera are measured by measuring the position and orientation of the radiation entrance window of each camera are measured in their passive state using a separate measuring system, which is capable of probing the radiation entrance window directly, and which delivers the position and orientation of the radiation entrance window in the world coordinate system. In this case, a purely external measurement of the camera position takes place, which includes the camera position and camera orientation. The disadvantage is that large, expanded auxiliary means with several measurement marks are required in order to measure the orientation. The auxiliary means are measuring means and must therefore be handled carefully, which is difficult to do in an industrial setting.
A further disadvantage is that the accuracy required for measurements with pixel or subpixel accuracy cannot be attained for large distances between the camera and the measurement object. When the auxiliary means are expanded, e.g., 400 mm with measurement marks on the outer points, and a measurement mark is determined with an accuracy of 0.3 mm, the radiation bundle may be used to calculate that, when the camera is 2000 mm away from the measurement object, an error of 3 mm occurs, which is often inadequate for applications. This situation is illustrated in FIG. 3.